{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"http://hilpisch.com/tpq_logo.png\" alt=\"The Python Quants\" width=\"35%\" align=\"right\" border=\"0\"><br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Derivatives Analytics with Python"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**_Chapter 8_**\n",
    "\n",
    "**Wiley Finance (2015)**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"http://hilpisch.com/images/derivatives_analytics_front.jpg\" alt=\"Derivatives Analytics with Python\" width=\"30%\" align=\"left\" border=\"0\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Yves Hilpisch\n",
    "\n",
    "The Python Quants GmbH\n",
    "\n",
    "<a href='mailto:analytics@pythonquants.com'>analytics@pythonquants.com</a>\n",
    "\n",
    "<a href='http://pythonquants.com'>www.pythonquants.com</a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import warnings\n",
    "warnings.simplefilter('ignore')\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Valuation by Integration & FFT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Value of Call Option   19.948\n"
     ]
    }
   ],
   "source": [
    "%run 08_m76/M76_valuation_INT.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Value of Call Option   19.948\n"
     ]
    }
   ],
   "source": [
    "%run 08_m76/M76_valuation_FFT.py"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calibration to 3 Maturities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   0 | [0.075 0.100 -0.500 0.100] |  35.009 |  35.009\n",
      "  50 | [0.075 0.300 -0.100 0.200] |  34.892 |  12.884\n",
      " 100 | [0.100 0.200 -0.200 0.100] |  24.976 |   9.283\n",
      " 150 | [0.125 0.100 -0.400 0.300] |   9.822 |   7.415\n",
      " 200 | [0.125 0.400 -0.500 0.200] |  53.397 |   5.581\n",
      " 250 | [0.150 0.200 0.000 0.100] |   5.022 |   3.822\n",
      " 300 | [0.175 0.100 -0.200 0.300] |  18.181 |   3.822\n",
      " 350 | [0.175 0.400 -0.300 0.200] |  46.957 |   3.822\n",
      " 400 | [0.200 0.300 -0.400 0.100] |  61.238 |   3.822\n",
      " 450 | [0.150 0.095 -0.206 0.198] |   3.798 |   3.798\n",
      " 500 | [0.160 0.008 -0.282 0.097] |   3.585 |   3.584\n",
      " 550 | [0.160 0.004 -0.273 0.113] |   3.584 |   3.584\n",
      " 600 | [0.160 0.005 -0.271 0.118] |   3.584 |   3.584\n",
      " 650 | [0.160 0.004 -0.286 0.118] |   3.584 |   3.584\n",
      " 700 | [0.160 0.003 -0.446 0.121] |   3.584 |   3.584\n",
      " 750 | [0.160 0.002 -0.611 0.112] |   3.583 |   3.583\n",
      " 800 | [0.160 0.001 -1.035 0.143] |   3.583 |   3.583\n",
      " 850 | [0.160 0.001 -1.469 0.193] |   3.583 |   3.583\n",
      " 900 | [0.160 0.001 -2.480 0.322] |   3.583 |   3.583\n",
      " 950 | [0.160 0.001 -4.268 0.563] |   3.583 |   3.583\n",
      "1000 | [0.160 0.001 -7.224 0.963] |   3.583 |   3.583\n",
      "1050 | [0.160 0.001 -16.274 2.190] |   3.583 |   3.583\n",
      "1100 | [0.160 0.001 -21.307 2.872] |   3.583 |   3.583\n",
      "1150 | [0.160 0.001 -30.691 4.145] |   3.583 |   3.583\n",
      "Warning: Maximum number of function evaluations has been exceeded.\n",
      "CPU times: user 45.6 s, sys: 34 ms, total: 45.6 s\n",
      "Wall time: 45.6 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "%run 08_m76/M76_calibration_FFT.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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OQ3+UiHQWkRwRuQg4MtZBRUPQa26RSOdc1Kvn6vXjx0OfPtCmTSE//JDoqJJD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\nJ0ralW5KdyFLZ5YLn+XCZ7n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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0989240c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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mdFk2m5OO303jFrX5zdDB9hSQSRrhtAEMUdVZMYqntDisDcAkpI0bYdw4149g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\nRR3TAkBEUkRks4is9F7vish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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0984fce150>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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FTlYWZ82ZU6nibSSOoSE3HNWtW5eHHnqIadOmlXhdVRERBg0axKJFiwD4+eefeeqpp/Z1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\neflyAARiWwMQkZ7ApUBTERk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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0984b8a7d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "generate_plot(opt, options);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calibration to Short Maturity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   0 | [0.100 0.100 -0.400 0.000] |  13.102 |  13.102\n",
      "  50 | [0.100 0.200 -0.200 0.000] |  13.074 |  10.498\n",
      " 100 | [0.100 0.300 0.000 0.020] |  15.648 |   7.988\n",
      " 150 | [0.100 0.500 -0.300 0.040] |   6.087 |   4.338\n",
      " 200 | [0.100 0.600 -0.100 0.060] |  12.132 |   4.338\n",
      " 250 | [0.125 0.100 -0.400 0.080] |   9.119 |   4.014\n",
      " 300 | [0.125 0.200 -0.200 0.100] |   9.139 |   4.014\n",
      " 350 | [0.125 0.300 0.000 0.120] |  10.455 |   3.779\n",
      " 400 | [0.125 0.500 -0.200 0.000] |   5.123 |   1.560\n",
      " 450 | [0.125 0.600 0.000 0.020] |  11.610 |   1.352\n",
      " 500 | [0.150 0.100 -0.300 0.040] |   6.047 |   1.352\n",
      " 550 | [0.150 0.200 -0.100 0.060] |   6.874 |   1.352\n",
      " 600 | [0.150 0.400 -0.400 0.080] |   3.860 |   1.352\n",
      " 650 | [0.150 0.500 -0.200 0.100] |   2.776 |   1.352\n",
      " 700 | [0.150 0.600 0.000 0.120] |   6.279 |   1.352\n",
      " 750 | [0.175 0.100 -0.200 0.000] |   5.391 |   1.352\n",
      " 800 | [0.175 0.200 0.000 0.020] |   5.842 |   1.352\n",
      " 850 | [0.175 0.400 -0.300 0.040] |   7.156 |   1.352\n",
      " 900 | [0.175 0.500 -0.100 0.060] |   5.342 |   1.352\n",
      " 950 | [0.175 0.700 -0.400 0.080] |  16.331 |   1.352\n",
      "1000 | [0.200 0.100 -0.200 0.100] |   8.506 |   1.352\n",
      "1050 | [0.200 0.200 0.000 0.120] |   8.725 |   1.352\n",
      "1100 | [0.200 0.400 -0.200 0.000] |  10.600 |   1.352\n",
      "1150 | [0.200 0.500 0.000 0.020] |   8.135 |   1.352\n",
      "1200 | [0.200 0.700 -0.300 0.040] |  17.515 |   1.352\n",
      "1250 | [0.130 0.587 -0.276 0.131] |   0.963 |   0.950\n",
      "1300 | [0.130 0.716 -0.227 0.124] |   0.923 |   0.916\n",
      "1350 | [0.130 0.894 -0.184 0.104] |   0.886 |   0.881\n",
      "1400 | [0.125 1.350 -0.138 0.015] |   0.613 |   0.599\n",
      "1450 | [0.124 1.390 -0.137 0.000] |   0.579 |   0.579\n",
      "1500 | [0.124 1.393 -0.137 0.000] |   0.579 |   0.579\n",
      "1550 | [0.124 1.393 -0.137 0.000] |   0.579 |   0.579\n",
      "Optimization terminated successfully.\n",
      "         Current function value: 0.578880\n",
      "         Iterations: 239\n",
      "         Function evaluations: 403\n",
      "CPU times: user 55.4 s, sys: 10 ms, total: 55.4 s\n",
      "Wall time: 55.4 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "%run 08_m76/M76_calibration_single.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.124, 1.393, -0.137, 0.000])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "opt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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cqmF/M9sN6G5m44BBaUcnEpFOnYKbdr77LvTpAwMHwlVXwXffRR2ZiIiElW6B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\nVfdgoHTzAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0984bb4f90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "generate_plot(opt, options);\n",
    "plt.savefig('../images/08_m76/M76_calibration_single.pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Monte Carlo Simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Value of Call Option  116.609\n",
      "CALL STRIKE         3000.000\n",
      "----------------------------\n",
      "Call Value by Int    269.749\n",
      "Call Value by FFT    269.733\n",
      "Difference FFT/Int    -0.016\n",
      "Call Value by MCS    270.503\n",
      "Difference MCS/Int     0.754\n",
      "----------------------------\n",
      "CALL STRIKE         3050.000\n",
      "----------------------------\n",
      "Call Value by Int    231.142\n",
      "Call Value by FFT    231.118\n",
      "Difference FFT/Int    -0.025\n",
      "Call Value by MCS    231.827\n",
      "Difference MCS/Int     0.685\n",
      "----------------------------\n",
      "CALL STRIKE         3100.000\n",
      "----------------------------\n",
      "Call Value by Int    194.905\n",
      "Call Value by FFT    194.890\n",
      "Difference FFT/Int    -0.015\n",
      "Call Value by MCS    195.531\n",
      "Difference MCS/Int     0.625\n",
      "----------------------------\n",
      "CALL STRIKE         3150.000\n",
      "----------------------------\n",
      "Call Value by Int    161.340\n",
      "Call Value by FFT    161.346\n",
      "Difference FFT/Int     0.006\n",
      "Call Value by MCS    161.905\n",
      "Difference MCS/Int     0.565\n",
      "----------------------------\n",
      "CALL STRIKE         3200.000\n",
      "----------------------------\n",
      "Call Value by Int    130.761\n",
      "Call Value by FFT    130.785\n",
      "Difference FFT/Int     0.024\n",
      "Call Value by MCS    131.247\n",
      "Difference MCS/Int     0.486\n",
      "----------------------------\n",
      "CALL STRIKE         3250.000\n",
      "----------------------------\n",
      "Call Value by Int    103.466\n",
      "Call Value by FFT    103.492\n",
      "Difference FFT/Int     0.026\n",
      "Call Value by MCS    103.823\n",
      "Difference MCS/Int     0.357\n",
      "----------------------------\n",
      "CALL STRIKE         3300.000\n",
      "----------------------------\n",
      "Call Value by Int     79.695\n",
      "Call Value by FFT     79.705\n",
      "Difference FFT/Int     0.010\n",
      "Call Value by MCS     79.906\n",
      "Difference MCS/Int     0.211\n",
      "----------------------------\n",
      "CALL STRIKE         3350.000\n",
      "----------------------------\n",
      "Call Value by Int     59.578\n",
      "Call Value by FFT     59.565\n",
      "Difference FFT/Int    -0.013\n",
      "Call Value by MCS     59.677\n",
      "Difference MCS/Int     0.099\n",
      "----------------------------\n",
      "CALL STRIKE         3400.000\n",
      "----------------------------\n",
      "Call Value by Int     43.104\n",
      "Call Value by FFT     43.076\n",
      "Difference FFT/Int    -0.028\n",
      "Call Value by MCS     43.161\n",
      "Difference MCS/Int     0.057\n",
      "----------------------------\n",
      "CALL STRIKE         3450.000\n",
      "----------------------------\n",
      "Call Value by Int     30.097\n",
      "Call Value by FFT     30.071\n",
      "Difference FFT/Int    -0.026\n",
      "Call Value by MCS     30.133\n",
      "Difference MCS/Int     0.036\n",
      "----------------------------\n",
      "CALL STRIKE         3500.000\n",
      "----------------------------\n",
      "Call Value by Int     20.232\n",
      "Call Value by FFT     20.224\n",
      "Difference FFT/Int    -0.008\n",
      "Call Value by MCS     20.288\n",
      "Difference MCS/Int     0.056\n",
      "----------------------------\n",
      "CALL STRIKE         3550.000\n",
      "----------------------------\n",
      "Call Value by Int     13.069\n",
      "Call Value by FFT     13.083\n",
      "Difference FFT/Int     0.015\n",
      "Call Value by MCS     13.161\n",
      "Difference MCS/Int     0.093\n",
      "----------------------------\n",
      "CALL STRIKE         3600.000\n",
      "----------------------------\n",
      "Call Value by Int      8.104\n",
      "Call Value by FFT      8.132\n",
      "Difference FFT/Int     0.028\n",
      "Call Value by MCS      8.210\n",
      "Difference MCS/Int     0.106\n",
      "----------------------------\n"
     ]
    }
   ],
   "source": [
    "%run 08_m76/M76_valuation_MCS.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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w7BFyctzKfsYY//g+l5SIZALdcLPVFnqbi4CFqvpadW9cFVZghMeXX8If/whF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\niYkVGMYYY2Ly/3NHrSjI71N1AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0984bc2950>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "results.plot(style=['b-', 'g^', 'ro'], grid=True)\n",
    "plt.ylabel('option value')\n",
    "plt.savefig('../images/08_m76/M76_value_comparison.pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"http://hilpisch.com/tpq_logo.png\" alt=\"The Python Quants\" width=\"35%\" align=\"right\" border=\"0\"><br>\n",
    "\n",
    "<a href=\"http://www.pythonquants.com\" target=\"_blank\">www.pythonquants.com</a> | <a href=\"http://twitter.com/dyjh\" target=\"_blank\">@dyjh</a>\n",
    "\n",
    "<a href=\"mailto:analytics@pythonquants.com\">analytics@pythonquants.com</a>\n",
    "\n",
    "**Python Quant Platform** |\n",
    "<a href=\"http://quant-platform.com\">http://quant-platform.com</a>\n",
    "\n",
    "**Derivatives Analytics with Python** |\n",
    "<a href=\"http://www.derivatives-analytics-with-python.com\" target=\"_blank\">Derivatives Analytics @ Wiley Finance</a>\n",
    "\n",
    "**Python for Finance** |\n",
    "<a href=\"http://python-for-finance.com\" target=\"_blank\">Python for Finance @ O'Reilly</a>"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python2",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
